Abstract

An analytic model of a Ti:LiNbO3 channel waveguide has been developed to predict conveniently the coupling coefficient of directional couplers based on near-field intensity measurements. This model is compared to experimental results at wavelengths of 0.63 and 0.81 μm and indicates an accuracy of predicting coupling coefficients within a factor of 2 without prior knowledge of the fabrication parameters.

© 1985 Optical Society of America

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References

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  1. R. C. Alferness, “Guided-Wave Devices for Optical Communication,” IEEE J. Quantum Electron. QE-17, 946 (1981).
    [Crossref]
  2. T. Suhara, Y. Handa, H. Nishihara, J. Koyama, “Analysis of Optical Channel Waveguides and Directional Couplers with Graded-Index Profile,” J. Opt. Soc. Am. 69, 807 (1979).
    [Crossref]
  3. A. Sharma, E. Sharma, I. C. Goyal, A. K. Ghatak, “The Variational Technique for Diffused Directional Couplers,” Opt. Commun. 34, 39 (1980).
    [Crossref]
  4. M. D. Feit, J. A. Fleck, L. McCaughan, “Comparison of Calculated and Measured Performance of Diffused Channel-Waveguide Couplers,” J. Opt. Soc. Am. 73, 1296 (1983).
    [Crossref]
  5. J. Ctyroky, M. Hofman, J. Janta, J. Schrofel, “3-D Analysis of LiNbO3: Ti Channel Waveguides and Directional Couplers,” IEEE J. Quantum Electron. QE-20, 400 (1984).
    [Crossref]
  6. C. H. Bulmer, W. K. Burns, “Polarization Characteristics of LiNbO3 Channel Waveguide Directional Couplers,” IEEE/OSA J. Lightwave Technol. LT-1, 227 (1983).
    [Crossref]
  7. M. Fukuma, J. Noda, H. Iwasaki, “Optical Properties in Titanium-Diffused LiNbO3 Strip Waveguides,” J. Appl. Phys. 49, 3693 (1978).
    [Crossref]
  8. C. T. Mueller, Ph.D. Dissertation, U. Southern California (1983).
  9. See, for example, G. B. Hocker, W. K. Burns, “Mode Dispersion in Diffused Channel Waveguides by the Effective Index Method,” Appl. Opt. 16, 113 (1977).
    [Crossref] [PubMed]
  10. E. M. Conwell, “Modes in Optical Waveguides Formed by Diffusion,” Appl. Phys. Lett. 23, 328 (1973).
    [Crossref]
  11. D. F. Nelson, V. J. McKenna, “Electromagnetic Modes of Anisotropic Dielectric Waveguides at p-n Junctions,” J. Appl. Phys. 38, 4057 (1967).
    [Crossref]
  12. L. M. Johnson, F. J. Leonberger, “Low-loss LiNbO3 Wave-guide Bends with Coherent Coupling,” Opt. Lett. 8, 111 (1983).
    [Crossref] [PubMed]
  13. C. T. Mueller, C. T. Sullivan, W. S. C. Chang, D. G. Hall, J. D. Zino, R. R. Rice, “An Analysis of the Coupling of an Injection Laser Diode to a Planar LiNbO3 Waveguide,” IEEE J. Quantum Electron. QE-16, 363 (1980).
    [Crossref]
  14. W. K. Burns, P. H. Klein, E. J. West, “Ti Diffusion in Ti: LiNbO3 Planar and Channel Optical Waveguides,” J. Appl. Phys. 50, 6175 (1979).
    [Crossref]
  15. R. J. Holmes, D. M. Smyth, “Titanium Diffusion into LiNbO3 as a Function of Stoichiometry,” J. Appl. Phys. 55, 3531 (1984).
    [Crossref]
  16. R. V. Schmidt, I. P. Kaminow, “Metal-Diffused Optical Waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458 (1974).
    [Crossref]
  17. Handbook of Chemistry and Physics (CRC Press, Cleveland, 1984–85).
  18. M. Minakata, S. Saito, M. Shibata, S. Miyazawa, “Precise Determination of Refractive-Index Changes in Ti-Diffused LiNbO3 Optical Waveguides,” J. Appl. Phys. 49, 4677 (1978).
    [Crossref]
  19. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1982).
  20. M. V. Hobden, J. Warner, “The Temperature Dependence of the Refractive Indices of Pure Lithium Niobate,” Phys. Lett. 22, 243 (1966).
    [Crossref]

1984 (2)

J. Ctyroky, M. Hofman, J. Janta, J. Schrofel, “3-D Analysis of LiNbO3: Ti Channel Waveguides and Directional Couplers,” IEEE J. Quantum Electron. QE-20, 400 (1984).
[Crossref]

R. J. Holmes, D. M. Smyth, “Titanium Diffusion into LiNbO3 as a Function of Stoichiometry,” J. Appl. Phys. 55, 3531 (1984).
[Crossref]

1983 (3)

1981 (1)

R. C. Alferness, “Guided-Wave Devices for Optical Communication,” IEEE J. Quantum Electron. QE-17, 946 (1981).
[Crossref]

1980 (2)

A. Sharma, E. Sharma, I. C. Goyal, A. K. Ghatak, “The Variational Technique for Diffused Directional Couplers,” Opt. Commun. 34, 39 (1980).
[Crossref]

C. T. Mueller, C. T. Sullivan, W. S. C. Chang, D. G. Hall, J. D. Zino, R. R. Rice, “An Analysis of the Coupling of an Injection Laser Diode to a Planar LiNbO3 Waveguide,” IEEE J. Quantum Electron. QE-16, 363 (1980).
[Crossref]

1979 (2)

W. K. Burns, P. H. Klein, E. J. West, “Ti Diffusion in Ti: LiNbO3 Planar and Channel Optical Waveguides,” J. Appl. Phys. 50, 6175 (1979).
[Crossref]

T. Suhara, Y. Handa, H. Nishihara, J. Koyama, “Analysis of Optical Channel Waveguides and Directional Couplers with Graded-Index Profile,” J. Opt. Soc. Am. 69, 807 (1979).
[Crossref]

1978 (2)

M. Fukuma, J. Noda, H. Iwasaki, “Optical Properties in Titanium-Diffused LiNbO3 Strip Waveguides,” J. Appl. Phys. 49, 3693 (1978).
[Crossref]

M. Minakata, S. Saito, M. Shibata, S. Miyazawa, “Precise Determination of Refractive-Index Changes in Ti-Diffused LiNbO3 Optical Waveguides,” J. Appl. Phys. 49, 4677 (1978).
[Crossref]

1977 (1)

1974 (1)

R. V. Schmidt, I. P. Kaminow, “Metal-Diffused Optical Waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458 (1974).
[Crossref]

1973 (1)

E. M. Conwell, “Modes in Optical Waveguides Formed by Diffusion,” Appl. Phys. Lett. 23, 328 (1973).
[Crossref]

1967 (1)

D. F. Nelson, V. J. McKenna, “Electromagnetic Modes of Anisotropic Dielectric Waveguides at p-n Junctions,” J. Appl. Phys. 38, 4057 (1967).
[Crossref]

1966 (1)

M. V. Hobden, J. Warner, “The Temperature Dependence of the Refractive Indices of Pure Lithium Niobate,” Phys. Lett. 22, 243 (1966).
[Crossref]

Alferness, R. C.

R. C. Alferness, “Guided-Wave Devices for Optical Communication,” IEEE J. Quantum Electron. QE-17, 946 (1981).
[Crossref]

Bulmer, C. H.

C. H. Bulmer, W. K. Burns, “Polarization Characteristics of LiNbO3 Channel Waveguide Directional Couplers,” IEEE/OSA J. Lightwave Technol. LT-1, 227 (1983).
[Crossref]

Burns, W. K.

C. H. Bulmer, W. K. Burns, “Polarization Characteristics of LiNbO3 Channel Waveguide Directional Couplers,” IEEE/OSA J. Lightwave Technol. LT-1, 227 (1983).
[Crossref]

W. K. Burns, P. H. Klein, E. J. West, “Ti Diffusion in Ti: LiNbO3 Planar and Channel Optical Waveguides,” J. Appl. Phys. 50, 6175 (1979).
[Crossref]

See, for example, G. B. Hocker, W. K. Burns, “Mode Dispersion in Diffused Channel Waveguides by the Effective Index Method,” Appl. Opt. 16, 113 (1977).
[Crossref] [PubMed]

Chang, W. S. C.

C. T. Mueller, C. T. Sullivan, W. S. C. Chang, D. G. Hall, J. D. Zino, R. R. Rice, “An Analysis of the Coupling of an Injection Laser Diode to a Planar LiNbO3 Waveguide,” IEEE J. Quantum Electron. QE-16, 363 (1980).
[Crossref]

Conwell, E. M.

E. M. Conwell, “Modes in Optical Waveguides Formed by Diffusion,” Appl. Phys. Lett. 23, 328 (1973).
[Crossref]

Ctyroky, J.

J. Ctyroky, M. Hofman, J. Janta, J. Schrofel, “3-D Analysis of LiNbO3: Ti Channel Waveguides and Directional Couplers,” IEEE J. Quantum Electron. QE-20, 400 (1984).
[Crossref]

Feit, M. D.

Fleck, J. A.

Fukuma, M.

M. Fukuma, J. Noda, H. Iwasaki, “Optical Properties in Titanium-Diffused LiNbO3 Strip Waveguides,” J. Appl. Phys. 49, 3693 (1978).
[Crossref]

Ghatak, A. K.

A. Sharma, E. Sharma, I. C. Goyal, A. K. Ghatak, “The Variational Technique for Diffused Directional Couplers,” Opt. Commun. 34, 39 (1980).
[Crossref]

Goyal, I. C.

A. Sharma, E. Sharma, I. C. Goyal, A. K. Ghatak, “The Variational Technique for Diffused Directional Couplers,” Opt. Commun. 34, 39 (1980).
[Crossref]

Hall, D. G.

C. T. Mueller, C. T. Sullivan, W. S. C. Chang, D. G. Hall, J. D. Zino, R. R. Rice, “An Analysis of the Coupling of an Injection Laser Diode to a Planar LiNbO3 Waveguide,” IEEE J. Quantum Electron. QE-16, 363 (1980).
[Crossref]

Handa, Y.

Hobden, M. V.

M. V. Hobden, J. Warner, “The Temperature Dependence of the Refractive Indices of Pure Lithium Niobate,” Phys. Lett. 22, 243 (1966).
[Crossref]

Hocker, G. B.

Hofman, M.

J. Ctyroky, M. Hofman, J. Janta, J. Schrofel, “3-D Analysis of LiNbO3: Ti Channel Waveguides and Directional Couplers,” IEEE J. Quantum Electron. QE-20, 400 (1984).
[Crossref]

Holmes, R. J.

R. J. Holmes, D. M. Smyth, “Titanium Diffusion into LiNbO3 as a Function of Stoichiometry,” J. Appl. Phys. 55, 3531 (1984).
[Crossref]

Iwasaki, H.

M. Fukuma, J. Noda, H. Iwasaki, “Optical Properties in Titanium-Diffused LiNbO3 Strip Waveguides,” J. Appl. Phys. 49, 3693 (1978).
[Crossref]

Janta, J.

J. Ctyroky, M. Hofman, J. Janta, J. Schrofel, “3-D Analysis of LiNbO3: Ti Channel Waveguides and Directional Couplers,” IEEE J. Quantum Electron. QE-20, 400 (1984).
[Crossref]

Johnson, L. M.

Kaminow, I. P.

R. V. Schmidt, I. P. Kaminow, “Metal-Diffused Optical Waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458 (1974).
[Crossref]

Klein, P. H.

W. K. Burns, P. H. Klein, E. J. West, “Ti Diffusion in Ti: LiNbO3 Planar and Channel Optical Waveguides,” J. Appl. Phys. 50, 6175 (1979).
[Crossref]

Koyama, J.

Leonberger, F. J.

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1982).

McCaughan, L.

McKenna, V. J.

D. F. Nelson, V. J. McKenna, “Electromagnetic Modes of Anisotropic Dielectric Waveguides at p-n Junctions,” J. Appl. Phys. 38, 4057 (1967).
[Crossref]

Minakata, M.

M. Minakata, S. Saito, M. Shibata, S. Miyazawa, “Precise Determination of Refractive-Index Changes in Ti-Diffused LiNbO3 Optical Waveguides,” J. Appl. Phys. 49, 4677 (1978).
[Crossref]

Miyazawa, S.

M. Minakata, S. Saito, M. Shibata, S. Miyazawa, “Precise Determination of Refractive-Index Changes in Ti-Diffused LiNbO3 Optical Waveguides,” J. Appl. Phys. 49, 4677 (1978).
[Crossref]

Mueller, C. T.

C. T. Mueller, C. T. Sullivan, W. S. C. Chang, D. G. Hall, J. D. Zino, R. R. Rice, “An Analysis of the Coupling of an Injection Laser Diode to a Planar LiNbO3 Waveguide,” IEEE J. Quantum Electron. QE-16, 363 (1980).
[Crossref]

C. T. Mueller, Ph.D. Dissertation, U. Southern California (1983).

Nelson, D. F.

D. F. Nelson, V. J. McKenna, “Electromagnetic Modes of Anisotropic Dielectric Waveguides at p-n Junctions,” J. Appl. Phys. 38, 4057 (1967).
[Crossref]

Nishihara, H.

Noda, J.

M. Fukuma, J. Noda, H. Iwasaki, “Optical Properties in Titanium-Diffused LiNbO3 Strip Waveguides,” J. Appl. Phys. 49, 3693 (1978).
[Crossref]

Rice, R. R.

C. T. Mueller, C. T. Sullivan, W. S. C. Chang, D. G. Hall, J. D. Zino, R. R. Rice, “An Analysis of the Coupling of an Injection Laser Diode to a Planar LiNbO3 Waveguide,” IEEE J. Quantum Electron. QE-16, 363 (1980).
[Crossref]

Saito, S.

M. Minakata, S. Saito, M. Shibata, S. Miyazawa, “Precise Determination of Refractive-Index Changes in Ti-Diffused LiNbO3 Optical Waveguides,” J. Appl. Phys. 49, 4677 (1978).
[Crossref]

Schmidt, R. V.

R. V. Schmidt, I. P. Kaminow, “Metal-Diffused Optical Waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458 (1974).
[Crossref]

Schrofel, J.

J. Ctyroky, M. Hofman, J. Janta, J. Schrofel, “3-D Analysis of LiNbO3: Ti Channel Waveguides and Directional Couplers,” IEEE J. Quantum Electron. QE-20, 400 (1984).
[Crossref]

Sharma, A.

A. Sharma, E. Sharma, I. C. Goyal, A. K. Ghatak, “The Variational Technique for Diffused Directional Couplers,” Opt. Commun. 34, 39 (1980).
[Crossref]

Sharma, E.

A. Sharma, E. Sharma, I. C. Goyal, A. K. Ghatak, “The Variational Technique for Diffused Directional Couplers,” Opt. Commun. 34, 39 (1980).
[Crossref]

Shibata, M.

M. Minakata, S. Saito, M. Shibata, S. Miyazawa, “Precise Determination of Refractive-Index Changes in Ti-Diffused LiNbO3 Optical Waveguides,” J. Appl. Phys. 49, 4677 (1978).
[Crossref]

Smyth, D. M.

R. J. Holmes, D. M. Smyth, “Titanium Diffusion into LiNbO3 as a Function of Stoichiometry,” J. Appl. Phys. 55, 3531 (1984).
[Crossref]

Suhara, T.

Sullivan, C. T.

C. T. Mueller, C. T. Sullivan, W. S. C. Chang, D. G. Hall, J. D. Zino, R. R. Rice, “An Analysis of the Coupling of an Injection Laser Diode to a Planar LiNbO3 Waveguide,” IEEE J. Quantum Electron. QE-16, 363 (1980).
[Crossref]

Warner, J.

M. V. Hobden, J. Warner, “The Temperature Dependence of the Refractive Indices of Pure Lithium Niobate,” Phys. Lett. 22, 243 (1966).
[Crossref]

West, E. J.

W. K. Burns, P. H. Klein, E. J. West, “Ti Diffusion in Ti: LiNbO3 Planar and Channel Optical Waveguides,” J. Appl. Phys. 50, 6175 (1979).
[Crossref]

Zino, J. D.

C. T. Mueller, C. T. Sullivan, W. S. C. Chang, D. G. Hall, J. D. Zino, R. R. Rice, “An Analysis of the Coupling of an Injection Laser Diode to a Planar LiNbO3 Waveguide,” IEEE J. Quantum Electron. QE-16, 363 (1980).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

E. M. Conwell, “Modes in Optical Waveguides Formed by Diffusion,” Appl. Phys. Lett. 23, 328 (1973).
[Crossref]

R. V. Schmidt, I. P. Kaminow, “Metal-Diffused Optical Waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458 (1974).
[Crossref]

IEEE J. Quantum Electron. (3)

R. C. Alferness, “Guided-Wave Devices for Optical Communication,” IEEE J. Quantum Electron. QE-17, 946 (1981).
[Crossref]

C. T. Mueller, C. T. Sullivan, W. S. C. Chang, D. G. Hall, J. D. Zino, R. R. Rice, “An Analysis of the Coupling of an Injection Laser Diode to a Planar LiNbO3 Waveguide,” IEEE J. Quantum Electron. QE-16, 363 (1980).
[Crossref]

J. Ctyroky, M. Hofman, J. Janta, J. Schrofel, “3-D Analysis of LiNbO3: Ti Channel Waveguides and Directional Couplers,” IEEE J. Quantum Electron. QE-20, 400 (1984).
[Crossref]

IEEE/OSA J. Lightwave Technol. (1)

C. H. Bulmer, W. K. Burns, “Polarization Characteristics of LiNbO3 Channel Waveguide Directional Couplers,” IEEE/OSA J. Lightwave Technol. LT-1, 227 (1983).
[Crossref]

J. Appl. Phys. (5)

M. Fukuma, J. Noda, H. Iwasaki, “Optical Properties in Titanium-Diffused LiNbO3 Strip Waveguides,” J. Appl. Phys. 49, 3693 (1978).
[Crossref]

D. F. Nelson, V. J. McKenna, “Electromagnetic Modes of Anisotropic Dielectric Waveguides at p-n Junctions,” J. Appl. Phys. 38, 4057 (1967).
[Crossref]

W. K. Burns, P. H. Klein, E. J. West, “Ti Diffusion in Ti: LiNbO3 Planar and Channel Optical Waveguides,” J. Appl. Phys. 50, 6175 (1979).
[Crossref]

R. J. Holmes, D. M. Smyth, “Titanium Diffusion into LiNbO3 as a Function of Stoichiometry,” J. Appl. Phys. 55, 3531 (1984).
[Crossref]

M. Minakata, S. Saito, M. Shibata, S. Miyazawa, “Precise Determination of Refractive-Index Changes in Ti-Diffused LiNbO3 Optical Waveguides,” J. Appl. Phys. 49, 4677 (1978).
[Crossref]

J. Opt. Soc. Am. (2)

Opt. Commun. (1)

A. Sharma, E. Sharma, I. C. Goyal, A. K. Ghatak, “The Variational Technique for Diffused Directional Couplers,” Opt. Commun. 34, 39 (1980).
[Crossref]

Opt. Lett. (1)

Phys. Lett. (1)

M. V. Hobden, J. Warner, “The Temperature Dependence of the Refractive Indices of Pure Lithium Niobate,” Phys. Lett. 22, 243 (1966).
[Crossref]

Other (3)

C. T. Mueller, Ph.D. Dissertation, U. Southern California (1983).

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1982).

Handbook of Chemistry and Physics (CRC Press, Cleveland, 1984–85).

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Figures (4)

Fig. 1
Fig. 1

(a) Geometry for the directional coupler interaction region. (b) Effective index method used to separate the channel waveguide into equivalent planar waveguides, G and G′, parallel to the crystal surface and parallel to the normal to the crystal surface, respectively.

Fig. 2
Fig. 2

Intensity profile parallel to the normal to the crystal surface (λ = 0.63 μm).

Fig. 3
Fig. 3

Intensity profile parallel to the crystal surface (λ = 0.63 μm).

Fig. 4
Fig. 4

Coupling length as a function of waveguide separation.

Equations (19)

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V = k D ( 2 n b Δ n ) 1 / 2 for Δ n n b ,
b = ( n eff n b ) / ( Δ n ) for Δ n n b ,
V = V b 1 / 2 2 W / D ,
b = ( n eff n b ) / ( n eff n b ) for Δ n n b ,
n eff = n b + Δ n b b for Δ n n b .
n ( x ) = n b + Δ n exp ( y / D ) for y 0 ,
E x ( y ) = A J u [ ξ exp ( y / 2 D ) ] , y 0 in LiNbO 3 ,
E x ( y ) = A J u [ ξ ] exp ( + υ y / 2 D ) , y 0 in the air ,
1 b b tan 1 1 / b 1 = 3 π / ( 8 V ) .
n ( x ) = n b + Δ n sech 2 ( x / W ) ,
E y = A [ sech ( x / W ) ] ( V + 1 1 ) / 2 ,
b = [ ( V 2 + 1 ) 1 / 2 1 ] 2 V .
D = 2 ( D t ) 1 / 2 ,
Δ n = C ( 0 ) d n 0 / d C .
0 C ( 0 ) exp ( y / D ) d y = α t .
d n 0 / d C = Δ n D / ( α t ) .
n 2 ( x ) = n b 2 + 2 n b Δ n [ g ( x + d / 2 ) + g ( x d / 2 ) ] ,
κ = k 2 n b Δ n 2 β · g ( x + d / 2 ) E * 1 · E 2 d x E * 1 · E 1 d x ,
κ = V 2 8 W [ b V 2 + 16 π 2 W 2 n b 2 λ 2 ] 1 / 2 · sech b V / 2 + 2 ( x + d / 2 W ) sech b V / 2 ( x d / 2 W ) d x sech b V ( x + d / 2 W ) d x .

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